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AIP conference proceedings

Macro-objectivation: a challenge in quantum field theory

L. Lanz

Published Jan 1, 2006• 0 citations
Publisher

Abstract

Thermodynamics of irreversible processes is taken as the phenomenological starting point for the description of macroscopic systems in quantum mechanics and state parameters, which are amenable to be attributed an objective meaning, are introduced inside non relativistic quantum field theory when the macroscopic system is locally at equilibrium. Conditions for these state parameters to obey a deterministic time evolution are indicated and discussed. The formalism is developed also considering the case of more component systems and bound states. The situation in which the deterministic dynamics of the state parameters breaks down is also envisaged and it is argued that in this case a stochastic generalisation of the theory is called for. First attempts in this direction are outlined, naturally leading to a rooting of the concept of microsystem inside both quantum theory and an objective phenomenological context.

DOI
10.1063/1.2219365

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Thermodynamics of irreversible processes is taken as the phenomenological starting point for the description of macroscopic systems in quantum mechanics and state parameters, which are amenable to be attributed an objective meaning, are introduced inside non relativistic quantum field theory when the macroscopic system is locally at equilibrium. Conditions for these state parameters to obey a deterministic time evolution are indicated and discussed. The formalism is developed also considering the case of more component systems and bound states. The situation in which the deterministic dynamics of the state parameters breaks down is also envisaged and it is argued that in this case a stochastic generalisation of the theory is called for. First attempts in this direction are outlined, naturally leading to a rooting of the concept of microsystem inside both quantum theory and an objective phenomenological context.
The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this relationship. This discussion requires some improvement of non-equilibrium statistical mechanics that is briefly presented. 1 Evolution of the atomistic idea: the new relationship micromacrosystems Classical physics was fully compatible with a deeply rooted, venerable philosophy: the wealth of objects called macrosystems, we become aware of in our experience at a certain space-time scale, arises by different structures of very many, very elementary, possibly of very few kinds, unavoidably elusive objects, microsystems at the previous scale; already in ancient times Lucretio called them primordia rerum. For a physicist the fundamental challenge is to learn about microsystems and discover the basic links; what remains is to face complexity: correlations of simple properties of single microsystems provide all describable variety. One expects that this scheme can be reproduced at smaller time-scales, to leave open the adventure of discerning more remote links. Since generally human being feels himself not completely fitting inside the
Abstract The deterministic and time-reversal symmetric dynamics of isolated quantum systems is at odds with irreversible equilibration observed in generic thermodynamic systems. Standard approaches at a reconciliation employ subjective restrictions on the space of observables or states and do not explain how a single macroscopic quantum system achieves equilibrium dynamically. We instead argue that quantum theory is an effective theory and requires corrections to accurately describe systems approaching the thermodynamic limit. We construct a stochastic extension of quantum theory which is practically identical to quantum mechanics for microscopic systems, yet allows individual macroscopic and isolated systems to objectively thermalize, generically. A fluctuation–dissipation relation guarantees physical consistency including norm preservation, energy conservation, no superluminal signalling and the emergence of microcanonical equilibrium. We further discuss the inclusion of objective collapse, thereby realizing a falsifiable theory of spontaneous universal irreversibility which describes the quantum-to-classical crossover dynamics of macroscopic quantum systems. The dynamics of the model describe spontaneous symmetry breaking, quantum state reduction and objective quantum thermalization for individual systems, while realizing emergent hybrid statistics for ensembles that integrate Born’s rule and microcanonical equilibrium.
The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of nonlinear and stochastic modifications of the Schroedinger equation. The proposed new dynamics is characterized by the feature of not contradicting any known fact about microsystems and of accounting, on the basis of a unique, universal dynamical principle, for wavepacket reduction and for the classical behavior of macroscopic systems. We recall the motivations for the new approach and we briefly review the other proposals to circumvent the above mentioned difficulties which appeared in the literature. In this way we make clear the conceptual and historical context characterizing the new approach. After having reviewed the mathematical techniques (stochastic differential calculus) which are essential for the rigorous and precise formulation of the new dynamics, we discuss in great detail its implications and we stress its relevant conceptual achievements. The new proposal requires also to work out an appropriate interpretation; a procedure which leads us to a reconsideration of many important issues about the conceptual status of theories based on a genuinely Hilbert space description of natural processes. We also discuss the possibility and the problems one meets in trying to develop an analogous formalism for the relativistic case. Finally we discuss the experimental implications of the new dynamics for various physical processes which should allow, in principle, to test it against quantum mechanics.
This paper has two aims: to provide a physical background of thermo field dynamics (TFD) and to present a review of the recent development of TFD. Macroscopic and thermal phenomena are considered from the unified viewpoint of microscopic quantum field theory. The concepts in quantum field theory such as renormalization and quasi-particles force us to take account of the time-dependence of the trace sum which has been ignored in the usual treatment of thermal situation. It is within this context that we review TFD. The applications of TFD to time-dependent non-equilibrium phenomena (the reservoir model and the self-interacting field model), show that we can obtain the master equation as well as the dissipative coefficient from the self-consistent renormalization condition. At the same time it is also shown that the final Gibbs distribution and the temperature can be derived, which implies that we obtain the equilibrium theory from the non-equilibrium one at the long-time limit.
It is argued that in the description of macroscopic systems inside quantum mechanics the study of the dynamics of selected degrees of freedom slowly varying on a suitable time scale, corresponding to relevant observables for the given reduced description, is particularly meaningful. A formalism developing these ideas in the more simple case of a microsystem interacting with a macroscopic system is briefly outlined, together with an application to the field of neutron optics. The obtained reduced description relies on a T-matrix formalism and has the property of complete positivity.